Open access Journal SINTA 3
THE METRIC DIMENSION OF CYCLE BOOK GRAPHS B_(C_(m,n) ) FORMED BY A COMMON PATH P_2
BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 20 No. 2 (2026) · pp. 1155–1166
- ISSN
- 2615-3017, 1978-7227
- Published
- 2026-01-26
- Publisher
- PATTIMURA UNIVERSITY
- Language
- eng
Abstract
This paper investigates the metric dimension of a class of graphs known as cycle books, denoted , which feature a shared path across multiple cycles. We focus on characterizing the minimum number of vertex subsets required so that each vertex in the graph can be uniquely identified by its distances to those subsets. To support our analysis, we present two propositions and a general theorem that establish the metric dimension for various configurations of cycle book graphs. Specifically, we prove that for, and for, while for. Furthermore, we provide a general result for: the metric dimension is when is odd and, or when is even and; and when is odd and. These findings contribute to the growing body of knowledge on metric properties in graph theory, particularly in structured and cyclic graph families.This paper investigates the metric dimension of a class of graphs known as cycle books, denoted , which feature a shared path across multiple cycles. We focus on characterizing the minimum number of vertex subsets required so that each vertex in the graph can be uniquely identified by its distances to those subsets. To support our analysis, we present two propositions and a general theorem that establish the metric dimension for various configurations of cycle book graphs. Specifically, we prove that for, and for, while for. Furthermore, we provide a general result for: the metric dimension is when is odd and, or when is even and; and when is odd and. These findings contribute to the growing body of knowledge on metric properties in graph theory, particularly in structured and cyclic graph families.This paper investigates the metric dimension of a class of graphs known as cycle books, denoted , which feature a shared path across multiple cycles. We focus on characterizing the minimum number of vertex subsets required so that each vertex in the graph can be uniquely identified by its distances to those subsets. To support our analysis, we present two propositions and a general theorem that establish the metric dimension for various configurations of cycle book graphs. Specifically, we prove that for, and for, while for. Furthermore, we provide a general result for: the metric dimension is when is odd and, or when is even and; and when is odd and. These findings contribute to the growing body of knowledge on metric properties in graph theory, particularly in structured and cyclic graph families.
Collaboration network of the authors
10 authors · 14 co-authorship links · 8 across different organisations
Hover or tap a name to highlight its co-authors. Double-click to open the author's page.
- Institut Teknologi Del
- Institut Teknologi Sepuluh Nopember
- Yogyakarta State University
- Binus University
- Different organisations
- Same organisation
- Affiliation unknown
- Thicker line = more joint articles · bigger circle = more articles
Show as table
| Co-author | Organisation | Joint articles |
|---|---|---|
| Marsigit Marsigit | Yogyakarta State University | 1 |
| Guslisnawati Guslisnawati | Yogyakarta State University | 1 |
| Adi Wibowo Panjaitan | Binus University | 1 |
| Frengki Simatupang | Institut Teknologi Del | 1 |
| Regina Ayunita Tarigan | Institut Teknologi Del | 1 |
| Darmaji Darmaji | Institut Teknologi Sepuluh Nopember | 1 |
Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.